Hmmmm -- I'd disagree with your vet. There's plenty of 'goodness' in real meat and a good quality dry food, as opposed to Chappie -- which is a pretty mediocre-quality food. Tinned food also is hardly the best for either losing weight or maintaining dental health (poor dental health can contribute significantly to heart disease). A quality dry food mixed with some white meat chicken that is boiled or grilled (NOT fried in oil or butter) and most importantly -- cutting back on the amount you feed -- will get the results you want. In general 'economical' food is also lower quality. I'd recommend going for something like James Wellbeloved which is moderate in price and simple but gives a balanced diet.
Dogs often turn up their noses if they know that eventually their owner tends to give in and offer more interesting things. Proper feeding is really giving the dog only 10-15 minutes to eat, no cajoling, then the food vanishes, no treats either, til the next *scheduled* meal. 99% of dogs will eat 99% of what is on offer by just sticking to such an approach.
If your dog is overweight, cut her rations by a third. If she isn't dropping some weight, gradually and safely, within a week or two, then cut her food in half. And cut out all treats -- most commercial treats have huge amounts of calories, especially things like Dentastix (one medium size dentastix has all the calories a cavalier would need in an entire DAY so they really need to be only occasional treats. Try moving your dog to healthy low calorie treats like sliced apple or pear, berries, carrots (but never grapes or raisins which in some dogs can cause acute renal failure).
There is information on getting dogs to lose weight in the Caring for your Cavalier section of the Library.
The easiest way for dogs to lose weight is for their owners to show a lighter hand with food at mealtime and cut the treats. Dogs don;t need treats. Being overweight will definitely shorten the life of a cavalier with heart problems as that heart has to work far harder and the valves will be put under much greater pressure. So when you feel pressured to give in and feed more, remember that you would surely prefer to have her around longer!
How much does she weigh? How much weight does your vet say she needs to lose (eg what weight should she be)?